This specification describes a loudspeaker with passively controlled directional radiation.
FIG. 1 shows a prior art end-fire acoustic pipe radiator suggested by FIG. 4 of Holland and Fahy, “A Low-Cost End-Fire Acoustic Radiator”, J. Audio Engineering Soc. Vol. 39, No. 7/8, 1991 July/August. An end-fire pipe radiator includes a pvc pipe 16 with an array of holes 12. If “a sound wave passes along the pipe, each hole acts as an individual sound source. Because the output from each hole is delayed, due to the propagation of sound along the pipe, by approximately l/c0 (where l is the distance between the holes and c0 is the speed of sound), the resultant array will beam the sound in the direction of the propagating wave. This type of radiator is in fact the reciprocal of the ‘rifle’ or ‘gun’ microphones used in broadcasting and surveillance.” (p. 540)
“The predictions of directivity from the mathematical model indicate that the radiator performs best when the termination impedance of the pipe is set to the characteristic impedance ρ0c0/S [where ρ0 is the density of air, c0 is the speed of sound, and S is the cross-sectional area of the pipe]. This is the condition that would be present if the pipe were of infinite length beyond the last hole. If Z0 [the termination impedance] were made to be in any way appreciably different from ρ0c0/S, instead of the radiator radiating sound predominantly in the forward direction, the reflected wave, a consequence of the impedance discontinuity, would cause sound to radiate backward as well. (The amount of ‘reverse’ radiation depends on how different Z0 is from ρ0c0/S.)” (p. 543)
“The two simplest forms of pipe termination, namely, open and closed both have impedances that are very different from ρ0c0/S and are therefore unsuitable for this system. . . . [An improved result with a closed end radiator] was achieved by inserting a wedge of open-cell plastic foam with a point at one end and a diameter about twice that of the pipe at the other. The complete wedge was simply pushed into the end of the pipe” (p. 543)
“Good examples of rifle microphones achieve more uniform results over a wider range of frequencies than the system of holes described. This is achieved by covering the holes, or sometimes a slot, with a flow-resistive material. The effect of this is similar to that described [elsewhere in the article] for the viscous flow resistance of the holes, and it allows the system to perform better at lower frequencies. The problem with this form of treatment is that the sensitivity of the system will suffer at higher frequencies” (p. 550).